Edit Profile (opens in new tab) Friedman, Avner Compute Distance To: Compute Author ID: friedman.avner Published as: Friedman, Avner; Friedman, A. External Links: MGP · Wikidata · GND · IdRef Documents Indexed: 540 Publications since 1956, including 36 Books 11 Contributions as Editor · 1 Further Contribution Biographic References: 1 Publication Co-Authors: 184 Co-Authors with 328 Joint Publications 4,625 Co-Co-Authors all top 5 Co-Authors 210 single-authored 43 Caffarelli, Luis Ángel 35 Hu, Bei 12 Chen, Xinfu 12 Velázquez, Juan J. L. 11 Reitich, Fernando 10 Alt, Hans Wilhelm 8 DiBenedetto, Emmanuele 8 McLeod, John Bryce 8 Yakubu, Abdul-Aziz 7 Fontelos López, Marco Antonio 7 Hao, Wenrui 6 Bazaliy, Borys V. 6 Cui, Shangbin 6 Kim, Yangjin 6 Ledzewicz, Urszula 6 Siewe, Nourridine 5 Anderson, Robert F. V. 5 Devinatz, Allen 5 Lai, Xiulan 5 Pinsky, Mark Allan 5 Xue, Chuan 4 Bellout, Hamid 4 Bensoussan, Alain 4 Brézis, Haïm 4 Craciun, Gheorghe 4 Huang, Chaocheng 4 Kao, Chiu-Yen 4 Lam, King-Yeung 4 Littman, Walter 4 Shinbrot, Marvin 4 Torelli, Alessandro 4 Turkington, Bruce E. 4 Vogelius, Michael S. 3 Aguda, Baltazar D. 3 Elliott, Charles M. 3 Herrero, Miguel Ángel 3 Huang, Shaoyun 3 Jiang, Lishang 3 Lacey, Andrew A. 3 Liu, Yong 3 Ross, David Stuart 2 Baiocchi, Claudio 2 Bazaliy, Yaroslaw B. 2 Chen, Duan 2 Dembele, Bassidy 2 Elliott, Robert James 2 Goel, Pranay 2 Green, J. Edward F. 2 Isakov, Victor M. 2 Jain, Harsh Vardhan 2 Kashdan, Eugene 2 Kaur, Balveen 2 Kinderlehrer, David 2 Lesinski, Gregory B. 2 Liao, Kang-Ling 2 Liu, Wenxiong 2 Lo, Wing-Cheong 2 Lungu, Edward M. 2 Marsh, Clay B. 2 Oswald, Luc 2 Ou, Biao 2 Pozzi, Gianni Arrigo 2 Satoskar, Abhay R 2 Schättler, Heinz Michael 2 Shih, Chih-Wen 2 Tao, Youshan 2 Tzavaras, Athanasios E. 2 Véron, Laurent 2 Vogel, Thomas Irvin 2 Yong, Jiongmin 2 Zhang, Jianhua 1 Aronson, Donald G. 1 Arsenescu, Razvan I. 1 Atiyah, Michael Francis 1 Bai, Xue-Feng 1 Banasiak, Jacek 1 Bao, Gang 1 Barbu, Viorel 1 Bassom, Andrew P. 1 Beckenbach, Edwin Ford 1 Bell, Jonathan 1 Bemelmans, Josef 1 Bernis, Francisco 1 Bojarski, Bogdan 1 Borisovich, Andreĭ Yur’evich 1 Borisyuk, Alla 1 Boushaba, Khalid 1 Brokate, Martin 1 Bruno, Oscar P. 1 Budd, Christopher John 1 Caligiuri, Michael A. 1 Chechkin, Gregory Aleksandrovich 1 Chiocca, E. Antonio 1 Chou, Ching-Shan 1 Conley, Elizabeth 1 Conwell, Darwin L. 1 Coskun, Huseyin 1 Crouser, Elliott D. 1 Day, Judy D. 1 de Bruijn, Nicolaas Govert ...and 112 more Co-Authors all top 5 Serials 48 Journal of Differential Equations 46 Transactions of the American Mathematical Society 38 Archive for Rational Mechanics and Analysis 34 Indiana University Mathematics Journal 26 Journal of Mathematical Analysis and Applications 21 Journal of Mathematics and Mechanics 20 SIAM Journal on Mathematical Analysis 13 Bulletin of Mathematical Biology 13 Mathematical Biosciences and Engineering 12 Communications in Partial Differential Equations 12 Journal of Theoretical Biology 11 The IMA Volumes in Mathematics and its Applications 10 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 10 Pacific Journal of Mathematics 10 SIAM Journal on Control and Optimization 10 Nonlinear Analysis. Theory, Methods & Applications 8 Discrete and Continuous Dynamical Systems. Series B 7 Journal of Mathematical Biology 7 SIAM Journal on Applied Mathematics 5 Duke Mathematical Journal 5 Proceedings of the American Mathematical Society 5 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 5 Proceedings of the National Academy of Sciences of the United States of America 5 Bulletin of the American Mathematical Society 4 Mathematical Biosciences 4 Journal of Functional Analysis 4 Journal für die Reine und Angewandte Mathematik 4 Kiberneticheskiĭ Sbornik. Novaya Seriya 4 European Journal of Applied Mathematics 4 Interfaces and Free Boundaries 3 Journal d’Analyse Mathématique 3 Acta Mathematica 3 Illinois Journal of Mathematics 3 Michigan Mathematical Journal 3 Notices of the American Mathematical Society 3 Lecture Notes in Mathematics 2 Communications on Pure and Applied Mathematics 2 American Journal of Mathematics 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Annales Polonici Mathematici 2 Mathematics of Operations Research 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Quarterly of Applied Mathematics 2 Asymptotic Analysis 2 SIAM Review 2 Discrete and Continuous Dynamical Systems 2 Multiscale Modeling & Simulation 2 Journal of Biological Dynamics 2 Mathematical Modelling of Natural Phenomena 2 Lecture Notes on Mathematical Modelling in the Life Sciences 2 Oxford Graduate Texts 1 Inverse Problems 1 Israel Journal of Mathematics 1 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 1 Reviews of Modern Physics 1 Rocky Mountain Journal of Mathematics 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Applied Mathematics and Optimization 1 Journal of the Faculty of Science. Section I A 1 Journal of Optimization Theory and Applications 1 Chinese Annals of Mathematics. Series B 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Journal of Non-Newtonian Fluid Mechanics 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Bollettino della Unione Matemàtica Italiana. Serie VII. B 1 Continuum Mechanics and Thermodynamics 1 Applied Mathematics. Series A (Chinese Edition) 1 Journal of Mathematical Sciences (New York) 1 Finance and Stochastics 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales (España) 1 SIAM Journal on Control 1 Regional Conference Series in Mathematics 1 Mathematics in Industry 1 Networks and Heterogeneous Media 1 Science China. Mathematics 1 Philosophical Transactions A. Royal Society of London 1 CBMS Regional Conference Series in Mathematics 1 Springer Undergraduate Texts in Mathematics and Technology all top 5 Fields 311 Partial differential equations (35-XX) 127 Biology and other natural sciences (92-XX) 73 Fluid mechanics (76-XX) 68 Calculus of variations and optimal control; optimization (49-XX) 39 Probability theory and stochastic processes (60-XX) 33 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 28 Mechanics of deformable solids (74-XX) 27 General and overarching topics; collections (00-XX) 25 Systems theory; control (93-XX) 19 Optics, electromagnetic theory (78-XX) 18 Ordinary differential equations (34-XX) 16 Classical thermodynamics, heat transfer (80-XX) 12 Statistics (62-XX) 11 Operations research, mathematical programming (90-XX) 10 Potential theory (31-XX) 7 Dynamical systems and ergodic theory (37-XX) 7 Operator theory (47-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Integral equations (45-XX) 5 Numerical analysis (65-XX) 3 History and biography (01-XX) 3 Real functions (26-XX) 3 Functional analysis (46-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Measure and integration (28-XX) 2 Special functions (33-XX) 2 Mechanics of particles and systems (70-XX) 2 Quantum theory (81-XX) 2 Astronomy and astrophysics (85-XX) 2 Geophysics (86-XX) 1 Combinatorics (05-XX) 1 Functions of a complex variable (30-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 455 Publications have been cited 10,869 times in 7,962 Documents Cited by ▼ Year ▼ Partial differential equations of parabolic type. Zbl 0144.34903Friedman, Avner 1,953 1964 Partial differential equations. Zbl 0224.35002Friedman, Avner 454 1969 Variational principles and free-boundary problems. Zbl 0564.49002Friedman, Avner 387 1982 Blow-up of positive solutions of semilinear heat equations. Zbl 0576.35068Friedman, Avner; McLeod, Bryce 341 1985 Stochastic differential equations and applications. Vol. 1. Zbl 0323.60056Friedman, Avner 323 1975 Higher order nonlinear degenerate parabolic equations. Zbl 0702.35143Bernis, Francisco; Friedman, Avner 185 1990 Variational problems with two phases and their free boundary. Zbl 0844.35137Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner 179 1984 Differential games. Zbl 0229.90060Friedman, Avner 173 1971 Hölder estimates for non-linear degenerate parabolic systems. Zbl 0549.35061DiBenedetto, Emmanuele; Friedman, Avner 162 1985 Stochastic differential equations and applications. Vol. 2. Zbl 0323.60057Friedman, Avner 160 1976 Classes of solutions of linear systems of partial differential equations of parabolic type. Zbl 0092.31002Friedman, Avner 140 1957 Analysis of a mathematical model for the growth of tumors. Zbl 0944.92018Friedman, Avner; Reitich, Fernando 136 1999 Nonlinear parabolic equations involving measures as initial conditions. Zbl 0527.35043Brézis, Haïm; Friedman, Avner 132 1983 The Stefan problem in several space variables. Zbl 0162.41903Friedman, A. 101 1968 Convexity of solutions of semilinear elliptic equations. Zbl 0599.35065Caffarelli, Luis A.; Friedman, Avner 95 1985 Generalized functions and partial differential equations. Zbl 0116.07002Friedman, A. 87 1963 Variational principles and free-boundary problems. Reprint. Zbl 0671.49001Friedman, Avner 86 1988 A free boundary problem arising in a model of wound healing. Zbl 0972.35193Chen, Xinfu; Friedman, Avner 82 2000 Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions. Zbl 0631.35041Friedman, Avner 74 1986 Regularity of the free boundary of a gas flow in an \(n\)-dimensional porous medium. Zbl 0439.76085Caffarelli, Luis A.; Friedman, Avner 73 1980 Symmetry-breaking bifurcation of analytic solutions to free boundary problems: An application to a model of tumor growth. Zbl 0983.35019Friedman, Avner; Reitich, Fernando 69 2001 Regularity of solutions of nonlinear degenerate parabolic systems. Zbl 0527.35038DiBenedetto, Emmanuele; Friedman, Avner 69 1984 Analysis of a mathematical model of the effect of inhibitors on the growth of tumors. Zbl 0998.92022Cui, Shangbin; Friedman, Avner 66 2000 Parabolic variational inequalities in one space dimension and smoothness of the free boundary. Zbl 0295.35045Friedman, Avner 65 1975 Identification of small inhomogeneities of extreme conductivity by boundary measurements: A theorem on continuous dependence. Zbl 0684.35087Friedman, Avner; Vogelius, Michael 65 1989 Foundations of modern analysis. Zbl 0198.07601Friedman, Avner 64 1970 Blow-up of solutions of nonlinear degenerate parabolic equations. Zbl 0619.35060Friedman, Avner; McLeod, Bryce 61 1986 The asymptotic behavior of gas in an \(n\)-dimensional porous medium. Zbl 0447.76076Friedman, Avner; Kamin, Shoshana 59 1980 Mathematical analysis of a model for the initiation of angiogenesis. Zbl 1020.35030Fontelos, Marco A.; Friedman, Avner; Hu, Bei 58 2002 Optimal stochastic switching and the Dirichlet problem for the Bellman equation. Zbl 0425.35046Evans, Lawrence C.; Friedman, Avner 57 1979 Bifurcation from stability to instability for a free boundary problem arising in a tumor model. Zbl 1087.92039Friedman, Avner; Hu, Bei 56 2006 A one phase Stefan problem. Zbl 0334.49002Friedman, Avner; Kinderlehrer, David 55 1975 Mathematical analysis and challenges arising from models of tumor growth. Zbl 1135.92013Friedman, Avner 55 2007 A free boundary problem for quasi-linear elliptic equations. Zbl 0554.35129Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner 54 1984 Partial regularity of the zero-set of solutions of linear and superlinear elliptic equations. Zbl 0593.35047Caffarelli, Luis A.; Friedman, Avner 54 1985 Free boundary problems for parabolic equations. I: Melting of solids. Zbl 0089.07801Friedman, Avner 53 1959 A free boundary problem for an elliptic-hyperbolic system: an application to tumor growth. Zbl 1054.35144Chen, Xinfu; Friedman, Avner 53 2003 The obstacle problem for the biharmonic operator. Zbl 0405.31007Caffarelli, Luis A.; Friedman, Avner 52 1979 Volterra integral equations in Banach space. Zbl 0147.12302Friedman, A.; Shinbrot, M. 51 1967 Remarks on the maximum principle for parabolic equations and its applications. Zbl 0103.06403Friedman, Avner 51 1958 Determining cracks by boundary measurements. Zbl 0697.35165Friedman, Avner; Vogelius, Michael 49 1989 Stability of solutions of chemotaxis equations in reinforced random walks. Zbl 1025.35005Friedman, Avner; Tello, J. Ignacio 48 2002 On the regularity of the solutions of nonlinear elliptic and parabolic systems of partial differential equations. Zbl 0078.27702Friedman, Avner 48 1958 A hierarchy of cancer models and their mathematical challenges. Zbl 1052.35094Friedman, Avner 47 2004 The boundary-value problem in domains with very rapidly oscillating boundary. Zbl 0938.35049Chechkin, Gregory A.; Friedman, Avner; Piatnitski, Andrey L. 45 1999 Symmetry-breaking bifurcations of free boundary problems in three dimensions. Zbl 1054.35145Fontelos, Marco A.; Friedman, Avner 45 2003 Continuity of the density of a gas flow in a porous medium. Zbl 0425.35060Caffarelli, Luis A.; Friedman, Avner 45 1979 Analysis of a mathematical model of the growth of necrotic tumors. Zbl 0984.35169Cui, Shangbin; Friedman, Avner 45 2001 Foundations of modern analysis. Reprint of the 1970 orig. Zbl 0557.46001Friedman, Avner 42 1982 Asymptotic stability for a free boundary problem arising in a tumor model. Zbl 1136.35106Friedman, Avner; Hu, Bei 42 2006 Stochastic differential games. Zbl 0208.39402Friedman, Avner 42 1972 The free boundary of a semilinear elliptic equation. Zbl 0552.35079Friedman, Avner; Phillips, Daniel 42 1984 The blow-up boundary for nonlinear wave equations. Zbl 0638.35053Caffarelli, Luis A.; Friedman, Avner 41 1986 A single point blow-up for solutions of semilinear parabolic systems. Zbl 0648.35042Friedman, Avner; Giga, Yoshikazu 41 1987 Analysis of a mathematical model of tumor lymphangiogenesis. Zbl 1060.92036Friedman, Avner; Lolas, Georgios 40 2005 Partial differential equations of parabolic type. Zbl 0173.12701Friedman, A. 40 1968 Stability and instability of Liapunov-Schmidt and Hopf bifurcation for a free boundary problem arising in a tumor model. Zbl 1161.35059Friedman, Avner; Hu, Bei 40 2008 Bifurcation for a free boundary problem modeling tumor growth by Stokes equation. Zbl 1136.35107Friedman, Avner; Hu, Bei 40 2007 Optimal control for variational inequalities. Zbl 0604.49007Friedman, Avner 39 1986 The time-harmonic Maxwell equations in a doubly periodic structure. Zbl 0759.35046Dobson, David; Friedman, Avner 39 1992 A free boundary problem for an elliptic-parabolic system: application to a model of tumor growth. Zbl 1031.35151Bazaliy, Borys V.; Friedman, Avner 38 2003 Nonlinear variational inequalities and differential games with stopping times. Zbl 0297.90120Bensoussan, Alain; Friedman, Avner 37 1974 Asymptotic estimates for the plasma problem. Zbl 0466.35033Caffarelli, Luis A.; Friedman, Avner 37 1980 Extinction properties of semilinear heat equations with strong absorption. Zbl 0655.35050Friedman, Avner; Herrero, Miguel A. 37 1987 Reinforcement problems for elliptic equations and variational inequalities. Zbl 0434.35079Brézis, Haïm; Caffarelli, Luis A.; Friedman, Avner 36 1980 Nonlinear stability of a quasi-static Stefan problem with surface tension: a continuation approach. Zbl 1072.35208Reitich, Fernando; Friedman, Avner 36 2001 Regularity of the free boundary for the one-dimensional flow of gas in a porous medium. Zbl 0439.76084Caffarelli, Luis A.; Friedman, Avner 36 1979 The shape of axisymmetric rotating fluid. Zbl 0439.35068Caffarelli, Luis A.; Friedman, Avner 35 1980 On the uniqueness in the inverse conductivity problem with one measurement. Zbl 0703.35165Friedman, Avner; Isakov, Victor 35 1989 Nonzero-sum stochastic differential games with stopping times and free boundary problems. Zbl 0368.93029Bensoussan, Alain; Friedman, Avner 34 1977 On integral equations of Volterra type. Zbl 0134.31502Friedman, A. 34 1963 The ill-posed Hele-Shaw model and the Stefan problem for supercooled water. Zbl 0621.35102DiBenedetto, Emmanuele; Friedman, Avner 33 1984 Differentiability of the blow-up curve for one dimensional nonlinear wave equations. Zbl 0593.35055Caffarelli, Luis A.; Friedman, Avner 32 1985 Axially symmetric jet flows. Zbl 0515.76017Alt, H. W.; Caffarelli, L. A.; Friedman, A. 32 1983 Analysis of a free-boundary tumor model with angiogenesis. Zbl 1344.35172Friedman, Avner; Lam, King-Yeung 32 2015 Stochastic differential equations and applications. Reprint of the 1975 and 1976 original editions. Zbl 1113.60003Friedman, Avner 32 2006 Interior estimates for parabolic systems of partial differential equations. Zbl 0082.30402Friedman, Avner 31 1958 Jets with two fluids. I. One free boundary. Zbl 0551.76013Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner 31 1984 Vortex rings: existence and asymptotic estimates. Zbl 0497.76031Friedman, Avner; Turkington, Bruce 31 1981 Systems of nonlinear wave equations with nonlinear viscosity. Zbl 0685.35070Friedman, Avner; Nečas, Jindřich 30 1988 Addendum to “Hölder estimates for nonlinear degenerate parabolic systems”. Zbl 0595.35065DiBenedetto, Emmanuelle; Friedman, Avner 29 1985 A mathematical model for pancreatic cancer growth and treatments. Zbl 1412.92154Louzoun, Yoram; Xue, Chuan; Lesinski, Gregory B.; Friedman, Avner 27 2014 A free boundary problem for a singular system of differential equations: An application to a model of tumor growth. Zbl 1036.34018Cui, Shangbin; Friedman, Avner 27 2003 Maxwell’s equations in a periodic structure. Zbl 0727.35131Chen, Xinfu; Friedman, Avner 27 1991 Global existence and asymptotic stability for an elliptic-parabolic free boundary problem: an application to a model of tumor growth. Zbl 1089.35079Bazaliy, Borys; Friedman, Avner 27 2003 Stochastic games and variational inequalities. Zbl 0285.90089Friedman, Avner 26 1973 Asymmetric jet flows. Zbl 0515.76018Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner 26 1982 Blow-up of solutions of nonlinear heat equations. Zbl 0653.35038Caffarelli, Luis A.; Friedman, Avner 26 1988 Bifurcation from stability to instability for a free boundary problem modeling tumor growth by Stokes equation. Zbl 1122.35013Friedman, Avner; Hu, Bei 25 2007 Compressible flows of jets and cavities. Zbl 0614.76074Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner 25 1985 Periodic behaviour for the evolutionary dam problem and related free boundary problems. Zbl 0624.35084DiBenedetto, Emmanuele; Friedman, Avner 24 1986 Optimal control for parabolic variational inequalities. Zbl 0624.49005Friedman, Avner 24 1987 Continuity of the temperature in the Stefan problem. Zbl 0406.35032Caffarelli, Luis A.; Friedman, Avner 24 1979 Isometric embedding of riemannian manifolds into Euclidean spaces. Zbl 0137.14901Friedman, A. 24 1965 One dimensional Stefan problems with nonmonotone free boundary. Zbl 0162.42001Friedman, A. 24 1968 Jet flows with gravity. Zbl 0561.76022Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner 24 1982 Asymptotic behavior of solutions of \(u_ t=\Delta u^ m\) as \(m\to \infty\). Zbl 0651.35039Caffarelli, Luis A.; Friedman, Avner 24 1987 On the existence of spatially patterned dormant malignancies in a model for the growth of non-necrotic vascular tumors. Zbl 1013.92024Friedman, Avner; Reitich, Fernando 23 2001 Symmetry-breaking bifurcations for free boundary problems. Zbl 1079.35012Borisovich, Andrei; Friedman, Avner 23 2005 Analyticity of the free boundary for the Stefan problem. Zbl 0329.35034Friedman, Avner 23 1976 Mathematical modeling of cancer treatment with radiation and PD-L1 inhibitor. Zbl 1431.35253Lai, Xiulan; Friedman, Avner 1 2020 Mathematical modeling in scheduling cancer treatment with combination of VEGF inhibitor and chemotherapy drugs. Zbl 1406.92312Lai, Xiulan; Friedman, Avner 4 2019 Antagonism and negative side-effects in combination therapy for cancer. Zbl 1418.35386Friedman, Avner; Lai, Xiulan 1 2019 Free boundary problems associated with cancer treatment by combination therapy. Zbl 1425.35240Friedman, Avner; Lai, Xiulan 1 2019 Rheumatoid arthritis – a mathematical model. Zbl 1406.92273Moise, Nicolae; Friedman, Avner 1 2019 The role of exosomes in pancreatic cancer microenvironment. Zbl 1394.92056Friedman, Avner; Hao, Wenrui 5 2018 Mathematical biology: modeling and analysis. Zbl 1404.92002Friedman, Avner 2 2018 Complex role of NK cells in regulation of oncolytic virus-bortezomib therapy. Zbl 1416.92051Kim, Yangjin; Yoo, Ji Young; Lee, Tae Jin; Liu, Joseph; Yu, Jianhua; Caligiuri, Michael A.; Kaur, Balveen; Friedman, Avner 1 2018 Mathematical model of chronic pancreatitis. Zbl 1404.92096Hao, Wenrui; Komar, Hannah M.; Hart, Phil A.; Conwell, Darwin L.; Lesinski, Gregory B.; Friedman, Avner 5 2017 The role of TNF-\(\alpha\) inhibitor in glioma virotherapy: a mathematical model. Zbl 1362.92034Ratajczyk, Elzbieta; Ledzewicz, Urszula; Leszczynski, Maciej; Friedman, Avner 4 2017 Granuloma formation in leishmaniasis: a mathematical model. Zbl 1368.92087Siewe, Nourridine; Yakubu, Abdul-Aziz; Satoskar, Abhay R; Friedman, Avner 4 2017 Mathematical modeling of liver fibrosis. Zbl 1348.92079Friedman, Avner; Hao, Wenrui 3 2017 Introduction to mathematical biology. Modeling, analysis, and simulations. Zbl 1351.92001Chou, Ching-Shan; Friedman, Avner 5 2016 Free boundary problems for systems of Stokes equations. Zbl 1357.35298Friedman, Avner 5 2016 Immune response to infection by Leishmania: a mathematical model. Zbl 1341.92042Siewe, Nourridine; Yakubu, Abdul-Aziz; Satoskar, Abhay R.; Friedman, Avner 4 2016 Analysis of a free-boundary tumor model with angiogenesis. Zbl 1344.35172Friedman, Avner; Lam, King-Yeung 32 2015 A mathematical model of atherosclerosis with reverse cholesterol transport and associated risk factors. Zbl 1334.92198Friedman, Avner; Hao, Wenrui 20 2015 A free boundary problem for steady small plaques in the artery and their stability. Zbl 1322.35181Friedman, Avner; Hao, Wenrui; Hu, Bei 10 2015 Free boundary problems in biology. Zbl 1353.35291Friedman, Avner 9 2015 Effects of CCN1 and macrophage content on glioma virotherapy: a mathematical model. Zbl 1335.92040Jacobsen, Karly; Russell, Luke; Kaur, Balveen; Friedman, Avner 4 2015 A PDE model for the dynamics of trail formation by ants. Zbl 1311.35325Fontelos, Marco A.; Friedman, Avner 3 2015 A mathematical model for pancreatic cancer growth and treatments. Zbl 1412.92154Louzoun, Yoram; Xue, Chuan; Lesinski, Gregory B.; Friedman, Avner 27 2014 Mathematical model of sarcoidosis. Zbl 1355.92049Hao, Wenrui; Crouser, Elliott D.; Friedman, Avner 17 2014 On a multiphase multicomponent model of biofilm growth. Zbl 1288.35388Friedman, Avner; Hu, Bei; Xue, Chuan 8 2014 A Bovine babesiosis model with dispersion. Zbl 1282.92019Friedman, Avner; Yakubu, Abdul-Aziz 3 2014 On the stability of steady states in a granuloma model. Zbl 1288.35482Friedman, Avner; Lam, King-Yeung 3 2014 Mathematical modeling of biological processes. Zbl 1302.92004Friedman, Avner; Kao, Chiu-Yen 3 2014 Mathematical model of renal interstitial fibrosis. Zbl 1355.92050Hao, Wenrui; Rovin, Brad H.; Friedman, Avner 1 2014 Modulation of the camp response by \(\mathrm{G}\alpha _i\) and \(\mathrm{G}\beta \gamma \): a computational study of G protein signaling in immune cells. Zbl 1298.92038Leander, R.; Friedman, A. 1 2014 Modeling prostate cancer response to continuous versus intermittent androgen ablation therapy. Zbl 1277.92013Jain, Harsh Vardhan; Friedman, Avner 12 2013 Anthrax epizootic and migration: persistence or extinction. Zbl 1303.92116Friedman, Avner; Yakubu, Abdul-Aziz 11 2013 A two-phase free boundary problem with discontinuous velocity: Application to tumor model. Zbl 1256.35208Chen, Duan; Friedman, Avner 5 2013 Mathematical methods and models in biomedicine. Zbl 1254.92046 4 2013 Epidemiological models with seasonality. Zbl 1345.92140Friedman, Avner 3 2013 Mathematical model of the roles of T cells in inflammatory bowel disease. Zbl 1272.92030Lo, Wing-Cheong; Arsenescu, Razvan I.; Friedman, Avner 2 2013 A mathematical model for cell-induced gel compaction in vitro. Zbl 1257.92018Green, J. E. F.; Bassom, Andrew P.; Friedman, Avner 2 2013 The role of CD200-CD200R in tumor immune evasion. Zbl 1330.92024Liao, Kang-Ling; Bai, Xue-Feng; Friedman, Avner 2 2013 The diffusion approximation for linear nonautonomous reaction-hyperbolic equations. Zbl 1276.35014Friedman, Avner; Hu, Bei; Keener, James P. 1 2013 A partial differential equation model of metastasized prostatic cancer. Zbl 1268.92059Friedman, Avner; Jain, Harsh Vardhan 1 2013 PDE problems arising in mathematical biology. Zbl 1260.49001Friedman, Avner 11 2012 Host demographic Allee effect, fatal disease, and migration: persistence or extinction. Zbl 1273.34052Friedman, Avner; Yakubu, Abdul-Aziz 9 2012 Hypoxia inducible factors-mediated inhibition of cancer by GM-CSF: a mathematical model. Zbl 1267.92043Chen, Duan; Roda, Julie M.; Marsh, Clay B.; Eubank, Timothy D.; Friedman, Avner 8 2012 Cancer as multifaceted disease. Zbl 1241.92038Friedman, A. 6 2012 A three dimensional model of wound healing: analysis and computation. Zbl 1395.92076Friedman, Avner; Hu, Bei; Xue, Chuan 6 2012 Modeling the inhibition of breast cancer growth by GM-CSF. Zbl 1337.92118Szomolay, Barbara; Eubank, Tim D.; Roberts, Ryan D.; Marsh, Clay B.; Friedman, Avner 6 2012 Conservation laws in mathematical biology. Zbl 1258.35142Friedman, Avner 4 2012 Asymptotic limit in a cell differentiation model with consideration of transcription. Zbl 1267.34078Friedman, Avner; Kao, Chiu-Yen; Shih, Chih-Wen 2 2012 Fatal disease and demographic Allee effect: population persistence and extinction. Zbl 1447.92337Friedman, Avner; Yakubu, Abdul-Aziz 1 2012 Asymptotic analysis for the narrow escape problem. Zbl 1252.35030Chen, Xinfu; Friedman, Avner 7 2011 A mathematical model for chronic wounds. Zbl 1259.92043Friedman, Avner; Xue, Chuan 7 2011 Tumor cells proliferation and migration under the influence of their microenvironment. Zbl 1259.92042Friedman, Avner; Kim, Yangjin 6 2011 Modeling the host response to inhalation anthrax. Zbl 1405.92143Day, Judy; Friedman, Avner; Schlesinger, Larry S. 3 2011 Interaction of tumor with its micro-environment: a mathematical model. Zbl 1197.92027Kim, Yangjin; Friedman, Avner 15 2010 Analysis of a mathematical model of ischemic cutaneous wounds. Zbl 1217.35195Friedman, Avner; Hu, Bei; Xue, Chuan 11 2010 Transformed epithelial cells and fibroblasts/myofibroblasts interaction in breast tumor: a mathematical model and experiments. Zbl 1204.92041Kim, Yangjin; Wallace, Julie; Li, Fu; Ostrowski, Michael; Friedman, Avner 6 2010 Mathematical model for optimal use of sulfadoxine-pyrimethamine as a temporary malaria vaccine. Zbl 1191.92025Dembele, Bassidy; Friedman, Avner; Yakubu, Abdul-Aziz 6 2010 Cell cycle control at the first restriction point and its effect on tissue growth. Zbl 1202.92024Friedman, Avner; Hu, Bei; Kao, Chiu-Yen 5 2010 Mathematical modeling of preadipocyte fate determination. Zbl 1406.92145Coskun, Huseyin; Summerfield, Taryn L. S.; Kniss, Douglas A.; Friedman, Avner 1 2010 A mathematical model for pattern formation of glioma cells outside the tumor spheroid core. Zbl 1405.92032Kim, Yangjin; Lawler, Sean; Nowicki, Michal O.; Chiocca, E. Antonio; Friedman, Avner 16 2009 Free boundary problems associated with multiscale tumor models. Zbl 1172.35080Friedman, A. 12 2009 Malaria model with periodic mosquito birth and death rates. Zbl 1342.92232Dembele, Bassidy; Friedman, Avner; Yakubu, Abdul-Aziz 10 2009 Asymptotic phases in a cell differentiation model. Zbl 1173.35590Friedman, Avner; Kao, Chiu-Yen; Shih, Chih-Wen 5 2009 Stability and instability of Liapunov-Schmidt and Hopf bifurcation for a free boundary problem arising in a tumor model. Zbl 1161.35059Friedman, Avner; Hu, Bei 40 2008 Tutorials in mathematical biosciences IV. Evolution and ecology. Tutorials presented at the Mathematical Bioscience Institute (MBI) in the years 2005–2006. Zbl 1130.92002 8 2008 A multiscale tumor model. Zbl 1157.35501Friedman, Avner 7 2008 Models of cellular regulation. Zbl 1231.92030Aguda, Baltazar D.; Friedman, Avner 6 2008 The extensional flow of a thin sheet of incompressible, transversely isotropic fluid. Zbl 1141.76009Green, J. Edward F.; Friedman, Avner 6 2008 The role of oxygen in tissue maintenance: mathematical modeling and qualitive analysis. Zbl 1152.35524Friedman, Avner; Hu, Bei 5 2008 A parabolic-hyperbolic quasilinear system. Zbl 1158.35004Chen, Xinfu; Friedman, Avner; Hu, Bei 2 2008 Mathematical analysis and challenges arising from models of tumor growth. Zbl 1135.92013Friedman, Avner 55 2007 Bifurcation for a free boundary problem modeling tumor growth by Stokes equation. Zbl 1136.35107Friedman, Avner; Hu, Bei 40 2007 Bifurcation from stability to instability for a free boundary problem modeling tumor growth by Stokes equation. Zbl 1122.35013Friedman, Avner; Hu, Bei 25 2007 Uniform convergence for approximate traveling waves in linear reaction-hyperbolic systems. Zbl 1133.35006Friedman, Avner; Hu, Bei 8 2007 Uniform convergence for approximate traveling waves in linear reaction-diffusion-hyperbolic systems. Zbl 1132.35006Friedman, Avner; Hu, Bei 3 2007 One-dimensional free boundary problem for actin-based propulsion of Listeria. Zbl 1104.92016Bazaliy, Borys; Bazaliy, Yaroslaw; Friedman, Avner 2 2007 Bifurcation from stability to instability for a free boundary problem arising in a tumor model. Zbl 1087.92039Friedman, Avner; Hu, Bei 56 2006 Asymptotic stability for a free boundary problem arising in a tumor model. Zbl 1136.35106Friedman, Avner; Hu, Bei 42 2006 Stochastic differential equations and applications. Reprint of the 1975 and 1976 original editions. Zbl 1113.60003Friedman, Avner 32 2006 A free boundary problem for a coupled system of elliptic, hyperbolic, and Stokes equations modeling tumor growth. Zbl 1106.35145Friedman, Avner 19 2006 Approximate traveling waves in linear reaction-hyperbolic equations. Zbl 1147.35330Friedman, Avner; Craciun, Gheorghe 12 2006 Homogenization of the cell cytoplasm: the calcium bidomain equations. Zbl 1128.35303Goel, Pranay; Sneyd, James; Friedman, Avner 8 2006 Tutorials in mathematical biosciences III. Cell cycle, prolifereation, and cancer. Zbl 1122.92030 4 2006 Differential games. Reprint of the 1971 original ed. Zbl 1225.91011Friedman, Avner 3 2006 Analysis of a mathematical model of tumor lymphangiogenesis. Zbl 1060.92036Friedman, Avner; Lolas, Georgios 40 2005 Symmetry-breaking bifurcations for free boundary problems. Zbl 1079.35012Borisovich, Andrei; Friedman, Avner 23 2005 A hyperbolic free boundary problem modeling tumor growth: asymptotic behavior. Zbl 1082.35166Chen, Xinfu; Cui, Shangbin; Friedman, Avner 17 2005 A model of intracellular transport of particles in an axon. Zbl 1068.92016Friedman, Avner; Craciun, Gheorghe 15 2005 The Hele-Shaw problem with surface tension in a half-plane: a model problem. Zbl 1075.76022Bazaliy, Borys V.; Friedman, Avner 13 2005 Generalized functions and partial differential equations. Reprint of the 1963 original. Zbl 1121.46001Friedman, Avner 12 2005 The Hele-Shaw problem with surface tension in a half-plane. Zbl 1076.76028Bazaliy, Borys V.; Friedman, Avner 11 2005 Tutorials in mathematical biosciences. I: Mathematical neuroscience. Zbl 1062.92008Borisyuk, Alla; Ermentrout, Bard G.; Friedman, Avner; Terman, David 5 2005 Symmetry-breaking bifurcations for free boundary problems. Zbl 1075.35117Friedman, Avner 2 2005 Mathematical analysis of a modular network coordinating the cell cycle and apoptosis. Zbl 1079.92023Craciun, Gheorghe; Aguda, Baltazar; Friedman, Avner 1 2005 Free boundary problems with surface tension conditions. Zbl 1153.35409Friedman, Avner 1 2005 A hierarchy of cancer models and their mathematical challenges. Zbl 1052.35094Friedman, Avner 47 2004 Symmetry-breaking bifurcations of charged drops. Zbl 1094.76022Fontelos, Marco A.; Friedman, Avner 17 2004 Free boundary problems arising in tumor models. Zbl 1162.35460Friedman, Avner 5 2004 A free boundary problem for an elliptic-hyperbolic system: an application to tumor growth. Zbl 1054.35144Chen, Xinfu; Friedman, Avner 53 2003 Symmetry-breaking bifurcations of free boundary problems in three dimensions. Zbl 1054.35145Fontelos, Marco A.; Friedman, Avner 45 2003 A free boundary problem for an elliptic-parabolic system: application to a model of tumor growth. Zbl 1031.35151Bazaliy, Borys V.; Friedman, Avner 38 2003 ...and 355 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 7,440 Authors 204 Friedman, Avner 53 Vazquez, Juan Luis 50 Mu, Chunlai 47 Hu, Bei 40 Winkler, Michael 39 Caffarelli, Luis Ángel 36 Shahgholian, Henrik 36 Zheng, Sining 35 Galaktionov, Victor Aleksandrovich 33 Xu, Shihe 33 Yi, Fahuai 32 Cui, Shangbin 32 Wang, Mingxin 28 Liu, Bingchen 28 Pao, Chia-Ven 27 Tao, Youshan 26 Cannon, John Rozier 26 Lin, Zhigui 25 Fasano, Antonio 25 Li, Fengjie 24 Macías-Díaz, Jorge Eduardo 24 Primicerio, Mario 23 Chen, Xinfu 23 Du, Lili 22 Peletier, Lambertus Adrianus 21 Ammari, Habib M. 21 Diaz Diaz, Jesus Ildefonso 21 Guo, Jong-Shenq 21 Shen, Wenxian 21 Souplet, Philippe 21 Velázquez, Juan J. L. 19 Herrero, Miguel Ángel 19 Rossi, Julio Daniel 19 Xie, Chunhong 18 Aronson, Donald G. 18 Du, Yihong 18 Mao, Xuerong 18 Véron, Laurent 18 Weiss, Georg Sebastian 18 Zaag, Hatem 17 Bao, Gang 17 Ding, Juntang 17 Hao, Wenrui 17 Karatzas, Ioannis 17 Yin, Hongming 16 Gao, Wenjie 16 Lions, Pierre-Louis 16 Perthame, Benoît 16 Valdinoci, Enrico 16 Yong, Jiongmin 15 Bögelein, Verena 15 DiBenedetto, Emmanuele 15 Escher, Joachim 15 Ishige, Kazuhiro 15 Kamin, Shoshana 15 Lesnic, Daniel 15 Mingione, Giuseppe 15 Taranets, Roman M. 15 Wu, Junde 15 Yin, Jingxue 14 Bertsch, Michiel 14 Chechkin, Gregory Aleksandrovich 14 Cheng, Jianfeng 14 Kang, Hyeonbae 14 Tarzia, Domingo Alberto 13 Karakhanyan, Aram L. 13 Lee, Ki-Ahm 13 Lenhart, Suzanne M. 13 Pascucci, Andrea 13 Qi, Yuanwei 13 Rodríguez-Bernal, Aníbal 13 Salsa, Sandro 13 Vasylyeva, Nataliya V. 13 Yang, Zhou 13 Zheng, Pan 12 Alessandrini, Giovanni 12 Ambrazevičius, Algirdas 12 Bandle, Catherine 12 Bellomo, Nicola 12 Beretta, Elena 12 De Angelis, Tiziano 12 Fila, Marek 12 Menozzi, Stéphane 12 Merle, Frank 12 Prüß, Jan Wilhelm 12 Suzuki, Takashi 12 Tesei, Alberto 11 Amann, Herbert 11 Bai, Meng 11 Brenner, Susanne Cecelia 11 Cao, Daomin 11 Ekström, Erik 11 Gol’dman, Nataliya L’vovna 11 Hayashi, Nakao 11 Hu, Guanghui 11 Kawohl, Bernd 11 Kim, Kwang Ik 11 King, John Robert 11 Ledzewicz, Urszula 11 Quirós Gracián, Fernando ...and 7,340 more Authors all top 5 Cited in 638 Serials 487 Journal of Differential Equations 468 Journal of Mathematical Analysis and Applications 217 Nonlinear Analysis. 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Series B 19 Japan Journal of Industrial and Applied Mathematics 19 Finance and Stochastics 19 Journal of Mathematical Fluid Mechanics ...and 538 more Serials all top 5 Cited in 57 Fields 5,468 Partial differential equations (35-XX) 977 Biology and other natural sciences (92-XX) 951 Probability theory and stochastic processes (60-XX) 858 Fluid mechanics (76-XX) 788 Numerical analysis (65-XX) 764 Calculus of variations and optimal control; optimization (49-XX) 568 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 414 Systems theory; control (93-XX) 377 Ordinary differential equations (34-XX) 332 Operator theory (47-XX) 315 Mechanics of deformable solids (74-XX) 266 Classical thermodynamics, heat transfer (80-XX) 213 Integral equations (45-XX) 169 Dynamical systems and ergodic theory (37-XX) 159 Global analysis, analysis on manifolds (58-XX) 149 Statistical mechanics, structure of matter (82-XX) 148 Functional analysis (46-XX) 132 Differential geometry (53-XX) 131 Optics, electromagnetic theory (78-XX) 129 Potential theory (31-XX) 97 Operations research, mathematical programming (90-XX) 71 Real functions (26-XX) 69 Statistics (62-XX) 55 Quantum theory (81-XX) 40 Measure and integration (28-XX) 40 Computer science (68-XX) 39 Harmonic analysis on Euclidean spaces (42-XX) 33 Information and communication theory, circuits (94-XX) 32 Geophysics (86-XX) 29 Approximations and expansions (41-XX) 27 Difference and functional equations (39-XX) 27 Astronomy and astrophysics (85-XX) 24 Functions of a complex variable (30-XX) 24 Mechanics of particles and systems (70-XX) 22 Integral transforms, operational calculus (44-XX) 20 Relativity and gravitational theory (83-XX) 14 General and overarching topics; collections (00-XX) 13 Convex and discrete geometry (52-XX) 10 History and biography (01-XX) 10 Nonassociative rings and algebras (17-XX) 10 Several complex variables and analytic spaces (32-XX) 10 General topology (54-XX) 9 Manifolds and cell complexes (57-XX) 8 Topological groups, Lie groups (22-XX) 8 Special functions (33-XX) 7 Combinatorics (05-XX) 7 Abstract harmonic analysis (43-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 5 Number theory (11-XX) 4 Group theory and generalizations (20-XX) 3 Algebraic geometry (14-XX) 3 Geometry (51-XX) 3 Mathematics education (97-XX) 2 Mathematical logic and foundations (03-XX) 2 Associative rings and algebras (16-XX) 2 Algebraic topology (55-XX) 1 Commutative algebra (13-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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